If $\alpha,\beta,\mu$ are roots of $2x^3-x^2+1=0$, the equation whose roots are $\alpha+1$, $\beta+1$, $\mu+1$ is found by:

1. Let $y=x+1$ be the new root, so each new root exceeds an old root by 1. 2. Rearranging gives $x=y-1$, expressing the old variable through the new one. 3. Substituting $x=y-1$ into $2x^3-x^2+1=0$ produces the equation satisfied by $y$. 4. In terms of the original letter that is the substitution $x\to x-1$. 5. Substituting $x+1$ instead shifts the roots down by 1; adding 1 to each coefficient changes the equation arbitrarily. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 6: Algebra_